How to add cascading shortcut in BetterTouchTool

I have a Logitech mouse with 2 side buttons which can be programmed to do anything in BTT. Although they work great, they do not trigger in certain apps (especially games).

So, my plan was to simply trigger F13 and F14 with those 2 buttons and then add shortcuts for F13 and F14 in other apps.

Example - 4th Mouse btn => F13 and in chrome F13 => Open new tab

But, this does not seem to work. Although, BTT recognizes that F13 has been clicked, chrome does not respond to it. Am Assuming this is because BTT stops after pressing F13 and the step of "F13 => Open new tab" never happens.

So, are there any fixes/alternatives to the above problem? Or maybe I am doing something wrong.